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\author{五六七}
\title{常微分方程第3周作业（2.4、2.6）}

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% 两个实际例子：探照灯镜面、人口问题。

% 作业：2.4: 1(1), 2(1), 3(1)。 2.6: 1(1), 2(1)。
% }

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\item 探照灯镜面：见DEBE目录。

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\item 人口问题：见DEBE目录。

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\item  (2.4)\#1(1): 
求解微分方程 $y' = \frac{2y-x}{2x-y}$. 

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{\color{red}解答：
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}

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\item  (2.4)\#2(1): 
利用适当的变换，求解微分方程 $y'=\cos(x-y)$. 

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{\color{red}解答：
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}

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\item  (2.4)\#3(1): 
求解微分方程 $y' = -y^2 -\frac{1}{4x^2}$. 

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{\color{red}解答：
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}

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\item  (2.6)\#1(1): 
求与曲线族 $x^2+y^2=Cx$ 相互正交的曲线族。 

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{\color{red}解答：
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\item  (2.6)\#2(1): 
求与曲线族 $x-2y=C$ 相交成 $\pi/4$ 角度的曲线族。 

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{\color{red}解答：
\begin{enumerate}[label=(\arabic*)]
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}

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\end{enumerate}

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